# A 45-45-90 triangle has a hypotenuse of length 14 units. What is the length of one of the legs?

Dec 24, 2015

$7 \sqrt{2}$ units

#### Explanation:

A 45-45-90 triangle is a right triangle whose legs are the same length. Let $l$ be that length. The Pythagorean theorem states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of its legs. Applying this, we have:

${l}^{2} + {l}^{2} = {14}^{2}$

$\implies 2 {l}^{2} = {14}^{2}$

$\implies {l}^{2} = {14}^{2} / 2$

$\implies l = \frac{14}{\sqrt{2}} = 7 \sqrt{2}$